Dear Rinku Mishra,

I can suggest you this book:

Shukla, P.K. and Mamun, A.A., 2001. Introduction to dusty plasma physics. CRC Press.

Please visit

https://books.google.ru/books?hl=en&lr=&id=_tk_CQAAQBAJ&oi=fnd&pg=PP1&dq=permittivity+of+dusty+plasma+&ots=u2ZtkKHx8j&sig=-IxOFTwWkOhAYy3DLrwaETG4yMk&redir_esc=y#v=onepage&q=permittivity%20of%20dusty%20plasma&f=false

or

http://physics.technion.ac.il/~plasma/publications/ebooks/books2/djvu_library/Plasma/Nonideal%20and%20dusty%20plasma/Shukla%20P.,%20Mamun%20A.%20Introduction%20to%20Dusty%20Plasma%20Physics%20(ISBN%20075030653X)(IoP,%202002)(275s).pdf

You can write it always 

epsilon_m = 1 + Xe + Xi + Xd ......  depending on your species.

Now based on your problem definition, you may find different versions of susceptibility  Xe, Xi, Xd etc...

For example, for epsilon_m = 1 - omega_p^2/omega^2   ..... you are assuming ions stationary (so no contribution by ion included) and no dispersion is taken into the account for electrons as well. 

This approach helps you build most complex dispersion relations very quickly.

You can read

http://newton.physics.uiowa.edu/~rmerlino/Grabbe_Merlino-Ch_52.pdf

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